Enhanced vehicle lateral control (lane following/lane keeping/lane changing control) for trailering vehicles

ABSTRACT

A method for providing a warning that a trailer being towed by a vehicle will cross out of a travel lane when in a curve for the current vehicle path prior to the vehicle entering the curve. The method determines that the vehicle is approaching the curve, determines a radius of curvature of the curve, determines a lane width of the travel lane, and identifying a length of the trailer. The method also determines a predicted steering angle of the vehicle necessary to follow the radius of curvature of the curve, a turn radius of the vehicle for traveling through the curve using the predicted steering angle, and a turn radius of the trailer using the turn radius of the vehicle. The method then determines whether the trailer will cross out of the travel lane based on the curvature of the curve and the turn radius of the trailer.

BACKGROUND OF THE INVENTION

Field of the Invention

This invention relates generally to a system and method for providing awarning that a trailer being towed by a vehicle will cross out of atravel lane when traveling through a curve for the current vehicle pathprior to the vehicle entering the curve and, more particularly, to asystem and method for providing a warning that a trailer being towed bya vehicle will cross out of a travel lane when traveling through a curvefor the current vehicle path prior to the vehicle entering the curve,where the system considers the turn radius of the vehicle and thetrailer, the width of the lane, the wheel base of the vehicle, thelength and width of the trailer and the curvature of the curve.

Discussion of the Related Art

The operation of modern vehicles is becoming more autonomous, i.e.,vehicles are able to provide driving control with less driverintervention. Cruise control systems have been on vehicles for a numberof years where the vehicle operator can set a particular speed of thevehicle, and the vehicle will maintain that speed without the driveroperating the throttle. Adaptive cruise control systems have beenrecently developed in the art where not only does the system maintainthe set speed, but also will automatically slow the vehicle down in theevent that a slower moving preceding vehicle is detected using varioussensors, such as radar and cameras. Certain modern vehicles also provideautonomous parking where the vehicle will automatically provide thesteering control for parking the vehicle. Some vehicle systems provideautomatic braking to prevent rear-end collisions. As vehicle systemsimprove, they will become more autonomous with the goal being acompletely autonomously driven vehicle, where future vehicles may employautonomous systems for lane changing, passing, turns away from traffic,turns into traffic, etc.

U.S. Pat. No. 8,170,739 issued May 1, 2012 to Lee, titled, PathGeneration Algorithm for Automated Lane Centering and Lane ChangingControl System, assigned to the Assignee of this application and hereinincorporated by reference, discloses a system for providing vehicle pathgeneration for automated lane centering and/or lane keeping purposes.The system detects lane markings on the roadway, generates a desiredvehicle path in the travel lane, and provides automatic steering thatmaintains the vehicle in the lane.

Although the system and method for providing path generation forautomated lane centering and lane keeping purposes disclosed in the '739patent is effective for steering the vehicle to stay in the travel lane,the system and method is not applicable for maintaining a towed vehiclein the lane even though the towing vehicle stays in the lane when thevehicle travels around a curve.

SUMMARY OF THE INVENTION

The present disclosure describes a system and method for providing awarning that a trailer being towed by a vehicle will cross out of atravel lane when traveling through a curve for the current vehicle pathprior to the vehicle entering the curve. The method includes determiningthat the vehicle is approaching the curve, determining a radius ofcurvature of the curve, determining a lane width of the travel lane, andidentifying a length of the trailer. The method also includesdetermining a predicted steering angle of the vehicle necessary tofollow the radius of curvature of the curve, determining a turn radiusof the vehicle for traveling through the curve using the predictedsteering angle, and determining a turn radius of the trailer using theturn radius of the vehicle. The method then determines whether thetrailer will at least partially cross out of the travel lane based onthe width of the lane, the width and length of the trailer, thecurvature of the curve and the turn radius of the trailer, and warn thedriver of the vehicle accordingly. Additionally, the method may provideturning recommendations to the driver once the vehicle has entered thecurve based on the current steering angle of the vehicle and a desiredsteering angle of the vehicle that will maintain the trailer in thetravel lane.

Additional features of the present invention will become apparent fromthe following description and appended claims, taken in conjunction withthe accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an illustration of a vehicle towing a trailer and approachinga curve in a travel lane;

FIG. 2 is an illustration showing the vehicle and the trailer travelingthrough the curve;

FIG. 3 is a flow chart diagram showing a process for warning a vehicledriver that the trailer may cross out of the lane when traveling througha curve;

FIG. 4 is a flow chart diagram similar to the flow chart diagram shownin FIG. 3, and including providing turning recommendations for thedriver so that the trailer does not cross out of the travel lane;

FIG. 5 is a block diagram of a path prediction system for providingautomated vehicle steering;

FIG. 6 is an illustration of a vehicle towing a trailer and travelingthrough a curve along a wide turn radius;

FIG. 7 is an illustration of a vehicle towing a trailer and travelingthrough a curve along a narrow turn radius;

FIG. 8 is a flow chart diagram showing a process for providing a pathfor the vehicle to follow for the wide turn radius; and

FIG. 9 is a flow chart diagram showing a process for providing a pathfor a vehicle to follow for the narrow turn radius.

DETAILED DESCRIPTION OF THE EMBODIMENTS

The following discussion of the embodiments of the invention directed toa system and method for providing a warning that a trailer being towedby a vehicle will cross out of a travel lane when traveling through acurve for the current vehicle path prior to the vehicle entering thecurve is merely exemplary in nature, and is in no way intended to limitthe invention or its applications or uses.

FIG. 1 is an illustration 10 showing a vehicle 14 towing a trailer 16 bya hitch 18 and traveling in a travel lane 12 of a roadway. The trailer16 is shown merely for representation purposes in that it can be anyvehicle being towed by the vehicle 14, such as boats, mobile homes, etc.The vehicle 14 is approaching a curve 20 in the lane 12 and is followingalong a travel path 22 at the center of the lane 12 that causes thevehicle 14 to stay within the lane 12. The vehicle 14 includes suitablesensors 24, such as cameras, radar, lidar, etc., that may be applicableto detect lane markings, objects, the curve 20, etc., consistent withthe discussion herein. The vehicle 14 also includes a map database 26, adisplay 30, a GPS unit 34 and a controller 28. The controller 28 isintended to represent all of the various modules, controllers,processors, electronic control units (ECUs), etc. that are necessary toperform and operate the various algorithms and processes discussedherein. The map database 26 stores map information at any level ofdetail that is available, such as the number of travel lanes, travellane patterns, etc. The travel path 22 can be displayed on the display30. The vehicle 14 and the trailer 16 are shown in phantom in theillustration 10 when traveling around the curve 20 along the path 22 toshow that the vehicle 14 may stay within the travel lane 12, but thetrailer 16 may cross out of the lane 12.

As is well understood, vehicles and trailers have a variety of sizes andlengths each possibly having a different wheel base l, trailer length,trailer width, hitch length, etc. that define the turn radius of thevehicle 14 and trailer 16 when going around the curve 20. Further,vehicle roadways may have different widths and roadway curves havedifferent radius of curvatures.

The present invention proposes identifying the predicted path of thevehicle 14 through the curve 20, whether the vehicle 14 is beingautonomously driven, semi-autonomously driven and/or mechanicallydriven, before the vehicle 14 enters the curve 20 to determine whetherthe trailer 16 will cross out of the lane 12, and if so, provide one ormore remedial actions. In one embodiment, if the controller 28determines that the predicted path of the vehicle 14 will cause thetrailer 16 to cross out of the lane 12, then the controller 28 willprovide a suitable warning, such as an icon on the display 30, hapticseat, haptic steering wheel, warning chimes, etc., prior to the vehicle14 reaching the curve 20, such as about 5 seconds before. The display 30may illustrate the predicted path of the vehicle 14 and the trailer 16.In another embodiment, the controller 28 may not only warn the vehicledriver that the trailer 16 may cross out of the lane 12, but also mayshow a path on the display 30 that the vehicle 14 should follow so thatthe trailer 16 does not cross out of the lane 12 when traveling throughthe curve 20 so as to provide a desired steering path for the driver. Inanother embodiment, where the vehicle 14 is being autonomously driven,the system will cause the vehicle 14 to be steered along a correctedlane following path or lane keeping path to prevent the trailer 16 fromcrossing out of the lane 12 in the curve 20.

FIG. 2 is an illustration 34 showing the vehicle 14 and the trailer 16traveling through the curve 20. In the illustration 34, for a particularvehicle steering angle δ and for a particular wheel base l of thevehicle 14, the turn radius R_(f) at the front of the vehicle 14 throughthe curve 20 can be calculated as:

$\begin{matrix}{R_{f} = {\frac{l}{\delta}.}} & (1)\end{matrix}$

Once the turn radius R_(f) of the vehicle 14 is known, the turn radiusR_(b) at the rear wheels of the vehicle 14, the turn radius R_(l) at thehitch point of the trailer 16, and the turn radius R_(t) at the rear ofthe trailer 16 can be calculated as:

R _(b)=√{square root over (R _(f) ²−(l+a ₁)²)},  (2)

R _(l)=√{square root over (R _(f) ²−(l+a ₁)² +b ₁ ²)},  (3)

R _(t)=√{square root over (R _(f) ²−(l+a ₁)² +b ₁ ² −b ₂ ²)},  (4)

where a₁ is the distance between the front wheels and the front bumperof the vehicle 14, b₁ is the length of the hitch 18, and b₂ is thelength of the trailer 16, which would be known or could be calculatedfrom a suitable sensor (not shown). It is noted that the turn radiusR_(t) of the trailer's end point is smaller than the turn radius R_(f)of the vehicle 14, and the turn radius R_(t) gets smaller as the lengthof the trailer 16 gets longer.

In order to determine whether the trailer 16 will cross out of thetravel lane 12 when in the curve 20, the radius of curvature of thecurve 20 and the width of the trailer 16 need to be known. The radius ofcurvature of the curve 20 can be obtained from cameras, the map database26, information from the GPS unit 32, or otherwise, and the turn radiusR_(f) is obtained by equation (1). Using these two radius values, thewidth of the trailer 16, the width of the lane 12 and equation (4), thecontroller 28 can determine whether part of the trailer 16 will crossout of the lane 12 in the curve 20 within some predetermined tolerance,such as +/−20 cm. For example, if the width of the lane 12 is 3.5 m, thecurve 20 has a 200 m radius of curvature, l is 2.9464 m, a₁ is 1.105 m,b₁ is 0.55 m, b₂ is 14.63 m, and the trailer width is 2.5908 m, thecontroller 28 can determine using equation (4) that the turn radiusR_(t) at a center of the trailer's end is 199.443 m, which is less thanthe radius of curvature of the curve 20. By knowing the width of thetrailer 16 and the width of the lane 12, the controller 28 can thendetermine that the end of the trailer 16 will cross out of the travellane 12, where the controller 28 can then provide a warning to thevehicle driver in advance.

FIG. 3 is a flow chart diagram 40 showing a process for determiningwhether to warn the vehicle driver that the trailer 16 will cross out ofthe lane 12 when traveling through the curve 20 along the currentvehicle path as discussed above. At box 42, the algorithm identifies acurve in the roadway at some predetermined time before the vehicle 14reaches the curve 20, such as 5 seconds, and also, identifies the radiusof the curve 20 and the lane width of the curve 20 at a certain sampletime. The algorithm identifies the length of the trailer 16 at box 44and determines the vehicle steering angle δ at box 46. The algorithmcalculates the trailer's turn radius R_(t) at box 48 in the mannerdiscussed above. The algorithm then compares the trailer's turn radiusR_(t) with the radius of the curve 20 at box 50, and then determineswhether the trailer 16 will cross out of the lane 12 using the width ofthe lane 12 and the width of the trailer 16 at decision diamond 52within the predetermined tolerance. If the trailer 16 will not cross outof the lane 12 at the decision diamond 52, then the algorithm does notprovide a warning and continues to monitor the vehicle path at box 54,and the algorithm ends at box 56. If the algorithm determines that thetrailer 16 will cross out of the lane 12 at the decision diamond 52,then the algorithm determines how soon the vehicle 14 will enter thecurve 20 at box 58, and provide the warning at box 60 if the vehicle 14will enter the curve 20 within some predetermined period of time, suchas 5 seconds. The algorithm can also show the predicted trailer path onthe display 30 at box 62 before the vehicle 14 enters the curve 20.

In addition to warning the vehicle driver that the trailer 16 may crossout of the travel lane 12 for the current vehicle path, the algorithmcan also provide recommendations for steering, such as display a vehiclepath that the vehicle driver can steer along, to prevent the trailer 16from crossing out of the travel lane 12. In order to perform thisfeature, the algorithm determines a desired steering angle δ_(desired)that will maintain the trailer 16 within the lane 12 once the vehicle 14has entered the curve 20 as:

$\begin{matrix}{\delta_{desired} = {\frac{2l}{{3R_{f}} - R_{t}}.}} & (5)\end{matrix}$

The algorithm then compares the desired steering angle δ_(desired) withthe current steering angle δ_(current) when the vehicle 14 has enteredthe curve 20, and if the desired steering angle δ_(desired) is differentthan the current steering angle δ_(current) outside of some tolerance,then the algorithm will display a change in the vehicle steering path toallow the driver to steer the vehicle 14 along the desired path toprevent the trailer 16 from crossing out of the lane 12. Alternately, orin addition to, the vehicle systems can provide audible instructions toprovide more or less left or right turning to maintain the desiredsteering angle δ_(desired).

FIG. 4 is a flow chart diagram 70 showing this embodiment of theinvention, where like boxes to the flow chart diagram 40 are identifiedby the same reference number. In the diagram 70, after the algorithmwarns the driver that the trailer 16 may travel outside of the lane 12,the algorithm will determine whether the vehicle 14 has entered thecurve 20 at decision diamond 72, and if not, return to the box 60 tocontinue warning the driver. If the vehicle 14 has entered the curve 20at the decision diamond 72, then the algorithm calculates the desiredsteering angle δ_(desired) to maintain the trailer 16 within the travellane 12 through the curve 20 at box 74, and then determines whether thedifference between the desired steering angle δ_(desired) and thecurrent steering angle δ_(current) is within the tolerance at decisiondiamond 76, where the algorithm ends at box 56 if it is. If thedifference between the desired steering angle δ_(desired) and thecurrent steering angle δ_(current) is outside of the tolerance at thedecision diamond 76, then the algorithm provides instructions for thedriver for a different steering angle at box 78, and shows the trailerpath at the box 62.

In a second aspect of the invention, the vehicle 14 is being drivenautonomously or semi-autonomously, where the vehicle is being controlledby determining the desired vehicle path and automatically steering thevehicle 14 along that path. In this embodiment, in order to prevent thetrailer 16 from crossing out of the lane 12 along the curve 20, thealgorithm generates a corrected lane following or lane keeping path, ifnecessary, for the vehicle 14 to be steered along through the curve 20considering the trailer's turn radius R_(t), the road curvature ρ, i.e.,the road radius, the lane width, the trailer length b₂, the vehiclewheel base l, etc., as discussed above.

The lane following or lane keeping algorithm may provide two differentpath planning approaches for navigating through the curve 20. In a firstturning approach, the algorithm calculates a vehicle path that providesa wide turn through the curve 20, where the turn starts at the beginningof the curve. This approach is illustrated in FIG. 5 by illustration 80showing the vehicle 14 as it enters the curve 20 and in phantom in thecurve 20. In this approach, the vehicle 14 begins its turn from thecurrent path 22 to a wide turn path 82 at the very beginning of thecurve 20 identified by a turn start point 84. Because this is a widerturn through the curve 20, the turn will end at point 86 before the endof the curve 20, where the vehicle 14 will begin traveling straight. Inthis embodiment, the start turn radius of the vehicle 14 at the point 84is R_(f), which is 200 m in the example above, the end turn radius ofthe vehicle 14 at the point 86 is

$\frac{{3R_{f}} - R_{t}}{2},$

which is 200.28 m in the example above, and the turn end point beforethe end of the curve 20 is:

$\begin{matrix}{\sqrt{R_{f}^{2} - \left( \frac{R_{f} + R_{t}}{2} \right)^{2}},} & (6)\end{matrix}$

which is 10.55 m before the end of the curve 20 in the example above.

A second turning approach provides a narrow turn from the path 22, buthaving a later turn start while the vehicle 14 is in the curve 20. Thisapproach is illustrated in FIG. 6 by illustration 90 showing the vehicle14 as it enters the curve 20 and in phantom in the curve 20. In thisapproach, the vehicle 14 begins its turn from the current path 22 to anarrow turn path 92 after the beginning of the curve 20 identified by aturn start point 94. Because this is a narrower turn through the curve20, the turn will end at point 96 at the very end of the curve 20 wherethe vehicle 14 will begin traveling straight. In this embodiment, thestart turn radius of the vehicle 14 at the point 94 is

$\frac{{3R_{f}} - R_{t}}{2},$

which is 200.28 m in the example above, the end turn radius of thevehicle 14 at the point 96 is R_(f), which is 200 m in the exampleabove, and the turn start point after the beginning of the curve 20 is:

$\begin{matrix}{\sqrt{R_{f}^{2} - \left( \frac{R_{f} + R_{t}}{2} \right)^{2}},} & (7)\end{matrix}$

which is 10.55 m after the beginning of the curve 20 in the exampleabove.

FIG. 7 is a schematic block diagram of a system 100 that providesautonomous path control for a vehicle when changing lanes, either on astraight road or a curved road, and lane centering in an autonomous orsemi-autonomous vehicle system. The discussion below is a generaldiscussion of providing a desired path in an autonomously driven orsemi-autonomously driven vehicle as more specifically discussed in the'739 patent. The system 100 includes a desired path generation processor102 that generates a desired steering path for the vehicle 14. For anypurpose, such as lane changing, curve navigation, object avoidance,etc., the desired steering path is represented as a series of lateraloffsets, heading angles and longitudinal distances over a time periodthat the steering change will take place.

The system 100 uses measured roadway parameters, such as vehicle lateraloffset y_(r), roadway curvature ρ and vehicle yaw angle φ_(r) withrespect to the vehicle's centered coordinate system at the pathgeneration processor 102. The roadway is modeled as a second orderpolynomial equation as:

y _(r)(x)=Ax ² +Bx+C, 0<x<x _(range)  (8)

where x_(range) represents the range of a forward vision camera on thevehicle 14.

From the geometric relationship between the roadway and the roadwayrepresentation of equation (8), the coefficients of equation (8) withthe measured roadway parameters y_(r), ρ and φ_(r) can be related as:

$\begin{matrix}{{A = \frac{\rho}{2}},} & (9) \\{{B = {\tan \mspace{11mu} \phi_{r}}},} & (10) \\{C = {{y_{r}(0)}.}} & (11)\end{matrix}$

Using the roadway lateral offset y_(r), the heading angle φ_(r) and theroadway curvature ρ, the path generation processor 102 generates asmooth desired path by solving a fifth order polynomial equationprovided as:

y _(d)(t)=a ₅ x _(d) ⁵(t)+a ₄ x _(d) ⁴(t)+a ₃ x _(d) ³(t)+a ₂ x _(d)²(t)+a ₁ x _(d) ¹(t)+a ₀.  (12)

The fifth order polynomial path generation captures the roadwayparameters y_(r), ρ and φ_(r) at the beginning and the end of the pathand guarantees the smoothness of the path up to the second order pathderivatives. In addition, the path can be obtained by a few simplealgebraic computations using the road geometry measurement, thus it doesnot require heavy computing power.

This path information including state variable x_(d), lateral positiony_(d), and heading angle φ_(d) is provided to a comparator 104 thatreceives a signal identifying a predicted vehicle path from a pathprediction processor 106, discussed below, and provides an error signalbetween the desired path and the predicted path. The lateral speedv_(y), the yaw angle φ and the lateral position y_(r) of the vehicle 14are predicted or estimated over the turn change completion time. Afterthe roadway model of equation (8) is obtained, the roadway lateralposition y_(r) and the yaw angle φ_(r) can be predicted at the pathprediction processor 106 using a vehicle dynamic model:

$\begin{matrix}{{{\overset{.}{x}}_{r} = {{A_{r}x_{r}} + {B_{r}\delta} + {G_{r}\rho}}},} & (13) \\{{z_{r} = {C_{r}x_{r}}},} & (14) \\{{with}\text{:}} & \; \\{x_{r} = \left\lbrack \begin{matrix}y_{r} & \phi_{r} & v_{y} & {\left. r \right\rbrack^{T},}\end{matrix} \right.} & (15) \\{B_{r} = \left\lbrack \begin{matrix}0 & 0 & \frac{C_{f}}{m} & {\left. \frac{{aC}_{f}}{I} \right\rbrack^{T},}\end{matrix} \right.} & (16) \\{{C_{r} = \begin{bmatrix}1 & 0 & 0 & 0 \\0 & 1 & 0 & 0\end{bmatrix}},} & (17) \\{G_{r} = \left\lbrack \begin{matrix}0 & v_{x} & 0 & {\left. 0 \right\rbrack^{T},}\end{matrix} \right.} & (18) \\{{A_{r} = \begin{bmatrix}0 & v_{x} & {- 1} & 0 \\0 & 0 & 0 & {- 1} \\0 & 0 & {- \frac{C_{f} + C_{r}}{{mv}_{x}}} & {\frac{{bC}_{r} - {aC}_{f}}{{mv}_{x}} - v_{x}} \\0 & 0 & \frac{{bC}_{r} - {aC}_{f}}{{Iv}_{x}} & {- \frac{{a^{2}C_{f}} + {b^{2}C_{r}}}{{Iv}_{x}}}\end{bmatrix}},} & (19)\end{matrix}$

where C_(f) and C_(r) are the concerning stiffnesses of the front wheelsand rear wheels of the vehicle 14, respectively, a and b are thedistances from the center of gravity of the vehicle 14 to the front andrear axles, respectively, m is the vehicle mass, δ is the steering angleand I_(z) is the moment of inertia around the center of mass of thevehicle 14 perpendicular to the plane where the vehicle 14 is located.

The error signal from the comparator 104 is sent to a lane changecontroller 108 that provides a steering angle command signal δ_(cmd) forpath steering that minimizes the error signal. The lane changecontroller 108 generates a sequence of future steering angle commandsδ_(cmd) that minimize the orientation and offset errors between thedesired vehicle path and the predicted vehicle path. A lateral motioncontrol algorithm in the controller 108 compares the predicted vehiclepath to the vehicle's desired path (x_(d), y_(d)), and calculates thesteering angle command signal δ_(cmd) by minimizing the path difference,where the steering angle command signal δ_(cmd) is obtained by:

$\begin{matrix}{{{\delta_{cmd}(k)} = \frac{\sum_{i = 0}^{N - 1}\; {\left( {{z_{d}\left( {k + i + 1} \right)} - {{CA}^{i + 1}{x(k)}}} \right)^{T}{Q\left( {k + i + 1} \right)}\left( {{CA}^{i}B} \right)}}{{\sum_{i = 0}^{N - 1}{\left( {{CA}^{i}B} \right){Q\left( {k + i + 1} \right)}\left( {{CA}^{i}B} \right)}} + {R(k)}}},} & (20)\end{matrix}$

and where x=[y φ v_(y), r]^(T), z_(d)(k)=[y_(d) φ_(d)]^(T), Q and R areweighting matrices used in the minimization with the system matricesdefinitions

A = e^(A_(r)t_(s)), B = ∫₀^(t_(s))e^(A_(r^(α)))B_(r)dα  and${C = {\begin{bmatrix}1 & 0 & 0 & 0 \\0 & 1 & 0 & 0\end{bmatrix}.}}\ $

The steering angle command signal δ_(cmd) is sent to a steering system110 that provides the steering control for a vehicle system 112. Thesteering system 110 receives the steering angle command signal δ_(cmd)and provides a steering torque command signal τ_(cmd) to achieve thedesired steering angle δ_(desired) as commanded.

As the vehicle 14 turns, various sensors on the vehicle 14, such as asteering angle sensor, speedometer and yaw rate sensor, provide measuredsignals of the motion of the vehicle 14. These measured vehicle motionsignals are sent from the vehicle system 112 to the desired pathgeneration processor 102. Inertial sensors, such as a speedometer, arate gyro and a steering angle sensor, can be used to measure vehiclestates, such as longitudinal speed v_(x), longitudinal accelerationa_(x), lateral acceleration a_(y), yaw rate r and steering angle δ. Thelateral speed v_(y) is estimated as:

$\begin{matrix}{{\begin{bmatrix}\overset{.}{{\overset{\bigwedge}{v}}_{y}} \\\overset{.}{\overset{\bigwedge}{r}}\end{bmatrix} = {{\begin{bmatrix}{- \frac{C_{f} + C_{r}}{{mv}_{x}}} & \frac{{bC}_{r} - {aC}_{f}}{{mv}_{x}} \\\frac{{bC}_{r} - {aC}_{f}}{{Iv}_{x}} & {- \frac{{a^{2}C_{f}} + {b^{2}C_{r}}}{{Iv}_{x}}}\end{bmatrix} \cdot \begin{bmatrix}{\overset{\bigwedge}{v}}_{y} \\\overset{\bigwedge}{r}\end{bmatrix}} + {\begin{bmatrix}\frac{C_{f}}{m} \\\frac{{aC}_{f}}{I}\end{bmatrix} \cdot \delta} + {K \cdot \begin{bmatrix}0 \\{r - \hat{r}}\end{bmatrix}}}},} & (21)\end{matrix}$

where r is a measured vehicle yaw rate, {circumflex over (v)}_(y) and{circumflex over (r)} are the estimated lateral speed and the vehicleyaw rate, respectively, and K is a yaw rate observer gain.

The vehicle motion information is also provided to a vehicle stateestimation processor 114 that provides estimated vehicle state signals,namely, lateral offset y, yaw angle φ, vehicle lateral speed v_(y) andvehicle yaw rate r. The vehicle state estimation processor 114 uses avehicle model to filter the estimated vehicle state signals. The statesignals are sent to the path prediction processor 106 that predicts thevehicle path for the next few instances in time based on thatinformation as discussed above. The path prediction processor 106estimates the vehicle future path based on the current vehicle speedv_(x), yaw rate r and steering angle δ.

The camera signals and the filtered sensor signals from the vehiclesystem 112 are also provided to a lane mark detection processor 116 thatcorrects the parameters of the lane markings based on the motion of thevehicle 14. The lane mark detection processor 116 recognizes the lanemarkings in the roadway and represents them with the parameters of lanecurvature, tangential angle and lateral offset, where the output of thelane mark detection processor 116 is the yaw angle φ_(r), the lateralposition y_(r), the curvature ρ of the roadway and a rate of change inthe roadway curvature Δρ of the roadway. The position of the lanemarkings relative to the vehicle 14 is then sent to the desired pathgeneration processor 102 through a roadway estimation processor 120 toprovide the desired path generation updating.

When the curve 20 is detected, the present invention proposes correctingthe desired steering path to prevent the trailer 16 from crossing out ofthe lane 12 as it travels around the curve 20. More particularly, thepath control algorithm revises the roadway curvature ρ and the rate ofchange in the roadway curvature Δρ with a new roadway curvature ρ_(new)and a new rate of change in roadway curvature Δρ_(new) in a pathcorrection processor 118 that is then used by the road estimationprocessor 120. If no curve is detected, then the roadway curvature ρ andthe rate of change in the roadway curvature Δρ pass unchanged throughthe processor 118. Specifically, for the wide turn path approach theprocessor 118 calculates the new roadway curvature ρ_(new) and the newrate of change in roadway curvature Δρ_(new) as:

$\begin{matrix}{{\rho_{new} = \frac{1}{R_{f}}},} & (22) \\{{{\Delta\rho}_{new} = \frac{2}{D\left( {R_{f} - R_{t}} \right)}},} & (23)\end{matrix}$

and for the narrow turn approach the processor 118 calculates the newroadway curvature ρ_(new) and the new rate of change in roadwaycurvature Δρ_(new) as:

$\begin{matrix}{{\rho_{new} = \frac{2}{{3R_{f}} - R_{t}}},} & (24) \\{{{\Delta\rho}_{new} = \frac{2}{D\left( {R_{f} - R_{t}} \right)}},} & (25)\end{matrix}$

where D is a tuning parameter to adjust for driver aggressiveness.

When the lane centering or lane keeping algorithm identifies the curve20, the algorithm uses the start point, the end point and the rate ofchange in the roadway curvature Δρ_(new) in combination with the pathgeneration operation in the path generation processor 102 for either thewide turn approach or the narrow turn approach, where the algorithm willbe previously programmed with one or the other of the wide turn approachor the narrow turn approach. For both of these approaches, the fifthorder polynomial of equation (12) is solved with different initial andboundary conditions by first normalizing the polynomial trajectory as:

$\begin{matrix}{{{y_{n}\left( x_{n} \right)} = {a_{0} + {a_{1}x_{n}} + {a_{2}x_{n}^{2}} + {a_{3}x_{n}^{3}} + {a_{4}x_{n}^{4}} + {a_{5}x_{n}^{5}}}},} & (26) \\{{{0 \leq x_{n}} = {\frac{x}{v_{x}\Delta \; T} \leq 1}},} & (27) \\{{y_{n} = \frac{y}{L}},} & (28)\end{matrix}$

where L is the lane width and ΔT is the time for the vehicle 14 totravel through the lane 12.

For the wide turn approach, initial conditions for the start point 84are given as:

$\begin{matrix}{{{y_{n}(0)} = 0},} & (29) \\{{{y_{n}^{\prime}(0)} = 0},} & (30) \\{{{y_{n}^{''}(0)} = \frac{\left( {v_{x}\Delta \; T} \right)^{2}}{R_{f}L}},} & (31)\end{matrix}$

and boundary conditions for the end point 86 are given as:

$\begin{matrix}{{{y_{n}(1)} = \frac{{y_{lane}\left( {v_{x}\Delta \; T} \right)} + L}{L}},} & (32) \\{{{y_{n}^{\prime}(1)} = {{y_{lane}^{\prime}\left( {v_{x}\Delta \; T} \right)} \cdot \frac{v_{x}\Delta \; T}{L}}},} & (33) \\{{{y_{n}^{''}(1)} = \frac{2\left( {v_{x}\Delta \; T} \right)^{2}}{\left( {{3R_{f}} - R_{t}} \right)L}},} & (34) \\{{y_{lane} = {{c_{3}x^{3}} + {c_{2}x^{2}} + {c_{1}x} + c_{0}}},} & (35)\end{matrix}$

and where c₀, c₁, c₂ and c₃ are measured values from a front camera.

For the narrow turn approach, different initial and boundary conditionsare used to solve the polynomial equation (26), where the initialconditions for the start point 94 are given as:

$\begin{matrix}{{{y_{n}(0)} = 0},} & (36) \\{{{y_{n}^{\prime}(0)} = 0},} & (37) \\{{{y_{n}^{''}(0)} = \frac{2\left( {v_{x}\Delta \; T} \right)^{2}}{\left( {{3R_{f}} - R_{t}} \right)L}},} & (38)\end{matrix}$

and the boundary conditions for the end point 96 are given as:

$\begin{matrix}{{{y_{n}(1)} = \frac{{y_{lane}\left( {v_{x}\Delta \; T} \right)} + L}{L}},} & (39) \\{{{y_{n}^{\prime}(1)} = {{y_{lane}^{\prime}\left( {v_{x}\Delta \; T} \right)} \cdot \frac{v_{x}\Delta \; T}{L}}},} & (40) \\{{y_{n}^{''}(1)} = {\frac{2\left( {v_{x}\Delta \; T} \right)^{2}}{R_{f}L}.}} & (41)\end{matrix}$

FIG. 8 is a flow chart diagram 130 showing a process for calculating thepath 82 for the wide turn approach when the vehicle 14 enters the curve20 as discussed above. At box 132, the algorithm obtains the roadwaycurvature ρ, the lane width, and the necessary measurements from the mapdatabase 26 and the forward looking camera on the vehicle 14. Thealgorithm obtains the length of the trailer 16 at box 134 and obtainsthe vehicle steering angle δ at box 136. The algorithm then calculatesthe trailer's turn radius R_(t) at box 138 and determines whether basedon the current path of the vehicle 14 the trailer 16 will cross out ofthe lane 12 in the curve 20 at decision diamond 140. If the trailer 16will not cross out of the lane 12 during the turn through the curve 20at the decision diamond 140, then the algorithm will cause the vehicle14 to continue along its current path at box 142, and the algorithm willend at box 144. If the trailer 16 will cross out of the lane 12 for thecurrent vehicle path at the decision diamond 140, then the algorithmcalculates the start turn radius R_(f) of the vehicle 14 at box 146,calculates the end turn radius

$\frac{{3R_{f}} - R_{t}}{2}$

of the vehicle 14 at box 148, and calculates the turn end point 86 fromequation (6) before the end of the curve 20 at box 150. The algorithmwill then update the initial boundary and conditions for the pathgeneration problem from equations (29)-(34) at box 152 and use thoseconditions for the path generation operation in the processor 92 at box154. The algorithm will then provide the necessary turning commands forthe new path at box 156 and report the new trailer path to the driver atbox 158.

FIG. 9 is a flow chart diagram 160 showing a process for calculating thepath 92 for the narrow turn approach when the vehicle 14 enters thecurve 20, as discussed above, that is the same as the steps in the flowchart diagram 130, except that the algorithm calculates the turn startpoint from equation (7) at box 162 instead of the end point of the turnat the box 150. Further, the start turn radius is

$\frac{{3R_{f}} - R_{t}}{2}$

at the box 146, the end turn radius is R_(f) at the box 148 and theinitial and boundary conditions at the box 152 are obtained fromequations (36)-(41).

As will be well understood by those skilled in the art, the several andvarious steps and processes discussed herein to describe the inventionmay be referring to operations performed by a computer, a processor orother electronic calculating device that manipulate and/or transformdata using electrical phenomenon. Those computers and electronic devicesmay employ various volatile and/or non-volatile memories includingnon-transitory computer-readable medium with an executable programstored thereon including various code or executable instructions able tobe performed by the computer or processor, where the memory and/orcomputer-readable medium may include all forms and types of memory andother computer-readable media.

The foregoing discussion discloses and describes merely exemplaryembodiments of the present invention. One skilled in the art willreadily recognize from such discussion and from the accompanyingdrawings and claims that various changes, modifications and variationscan be made therein without departing from the spirit and scope of theinvention as defined in the following claims.

What is claimed is:
 1. A method for identifying whether a trailer beingtowed by a tow vehicle may at least partially cross out of a travel laneof a curve that the vehicle is traveling along, said method comprising:determining that the vehicle is approaching the curve in the travellane; determining a radius of curvature of the curve and a lane width ofthe travel lane; determining a length and a width of the trailer;determining a predicted steering angle of the vehicle necessary tofollow the radius of curvature of the curve; determining a turn radiusof the vehicle for traveling through the curve using the predictedsteering angle; determining a turn radius of a rear end point of thetrailer using the turn radius of the vehicle; determining that thetrailer will cross out of the travel lane based on the curvature of thecurve and the turn radius of the rear end point of the trailer; andwarning a driver of the vehicle that the trailer may cross out of thetravel lane before the vehicle reaches the curve.
 2. The methodaccording to claim 1 wherein determining a turn radius of a rear endpoint of the trailer includes determining a turn radius of the rear endof the trailer based on the turn radius of the vehicle, a wheel base ofthe vehicle, a distance from front wheels of the vehicle to a frontbumper of the vehicle, a hitch length between the vehicle and thetrailer, and the length of the trailer.
 3. The method according to claim2 wherein determining a turn radius of the rear end point of the trailerincludes using the equation:R _(t)=√{square root over (R _(f) ²(l+a ₁)² +b ₁ ² −b ₂ ²)} where R_(t)is the turn radius of the rear end point of the trailer, l is the wheelbase of the vehicle, a₁ is the distance from the front bumper to thefront wheels of the vehicle, b₁ is the hitch length and b₂ is the lengthof the trailer, R_(f) is the turn radius of a front tip of the vehicle,and is determined as $\frac{l}{\delta},$ where δ is the steering angle.4. The method according to claim 1 wherein determining that the trailerwill cross out of the travel lane includes comparing the turn radius ofthe rear end point of the trailer to the curvature of the curve usingthe width of the trailer and a width of the travel lane.
 5. The methodaccording to claim 1 wherein determining that the vehicle is approachingthe curve includes using information from a camera on the vehicle,sensors on the vehicle, a GPS unit, and/or a map database, and includesdetermining when the vehicle will enter the curve.
 6. The methodaccording to claim 1 wherein warning the driver that the trailer maycross out of the travel lane includes providing one or more of a warningicon on a display, haptic seat, haptic steering wheel, and warningchimes.
 7. The method according to claim 1 further comprising displayinga path of the vehicle and a path of the trailer traveling around thecurve for a current steering angle.
 8. The method according to claim 1further comprising displaying a path of the vehicle and a path of thetrailer traveling around the curve for a desired steering angle.
 9. Themethod according to claim 1 wherein warning the driver that the trailermay cross out of the travel lane includes warning the driver at leastfive seconds before the vehicle enters the curve at a current vehiclespeed.
 10. The method according to claim 1 further comprisingdetermining that the vehicle has entered the curve and providing thedriver of the vehicle with a turn recommendation for more or lessturning if it is determined that the trailer may cross out of the travellane.
 11. The method according to claim 10 further comprisingcalculating a desired steering angle of the vehicle after the vehiclehas entered the curve that causes the trailer to stay within the lane,determining whether a difference between the desired steering angle anda current steering angle is within some predetermined tolerance, andproviding the recommendation of more or less turning if the differenceis outside of the tolerance.
 12. A method for determining a steeringangle range that a trailer being towed by a tow vehicle may at leastpartially cross out of a travel lane of a curve that the vehicle istraveling along after the vehicle has entered the curve, said methodcomprising: determining that the vehicle has entered the curve;determining a current steering angle of the vehicle; determining adesired steering angle of the vehicle that will maintain the trailerwithin the travel lane; determining whether a difference between thecurrent steering angle and the desired steering angle is within apredetermined tolerance; and providing a turn recommendation to avehicle driver for providing more or less turning to cause the driver tochange the current steering angle of the vehicle to be within thetolerance so that the trailer does not cross out of the travel lane inthe curve.
 13. The method according to claim 12 wherein determining adesired steering angle includes determining a turn radius of a rear endpoint of the trailer using a turn radius of the vehicle, a wheel base ofthe vehicle, a distance from front wheels of the vehicle to a frontbumper of the vehicle, a hitch length between the vehicle and thetrailer, a length of the trailer, a radius of curvature of the curve,and a lane width of the travel lane.
 14. The method according to claim13 wherein determining a turn radius of the rear end point of thetrailer includes using the equation:R _(t)=√{square root over (R _(f) ²(l+a ₁)² +b ₁ ² −b ₂ ²)} where R_(t)is the turn radius of the rear end point of the trailer, l is the wheelbase of the vehicle, a₁ is the distance from the front bumper to thefront wheels of the vehicle, b₁ is the hitch length and b₂ is the lengthof the trailer, R_(f) is the turn radius of a front tip of the vehicle,and is determined as $\frac{l}{\delta},$ where δ is the steering angle.15. The method according to claim 12 further comprising displaying apath of the vehicle and a path of the trailer traveling around the curvefor the current steering angle.
 16. The method according to claim 12further comprising displaying a path of the vehicle and a path of thetrailer traveling around the curve for the desired steering angle. 17.The method according to claim 12 further comprising warning the driverif the difference between the current steering angle and the desiredsteering angle is outside of the predetermined tolerance.
 18. A methodfor identifying whether a trailer being towed by a tow vehicle may atleast partially cross out of a travel lane of a curve that the vehicleis traveling along, said method comprising: determining that the vehicleis approaching the curve in the travel lane; determining a radius ofcurvature of the curve, a lane width of the travel lane, a wheel base ofthe vehicle, a distance from front wheels of the vehicle to a frontbumper of the vehicle, a hitch length between the vehicle and thetrailer, and a length of the trailer; determining a predicted steeringangle of the vehicle necessary to follow the radius of curvature of thecurve; determining a turn radius of the vehicle for traveling throughthe curve using the predicted steering angle and the wheel base;determining a turn radius of a rear end point of the trailer using theturn radius of the vehicle, the wheel base of the vehicle, the distancefrom the front wheels of the vehicle to the front bumper of the vehicle,the hitch length and the length of the trailer; determining that thetrailer will cross out of the travel lane based on the curvature of thecurve, the turn radius of the rear end point of the trailer, the widthof the trailer and the width of the travel lane; warning a driver of thevehicle that the trailer may cross out of the travel lane before thevehicle reaches the curve; determining that the vehicle has reached thecurve; determining a current steering angle of the vehicle; determininga desired steering angle of the vehicle based on the turn radius of thevehicle and the turn radius of the rear end point of the trailer;determining whether a difference between the current steering angle andthe desired steering angle is outside of a predetermined tolerance; andproviding a turn recommendation to the vehicle driver if the differenceis outside of the tolerance.
 19. The method according to claim 18wherein determining a turn radius of the rear end of the trailerincludes using the equation:R _(t)=√{square root over (R _(f) ²(l+a ₁)² +b ₁ ² −b ₂ ²)} where R_(t)is the turn radius of the rear end point of the trailer, l is the wheelbase of the vehicle, a₁ is the distance from the front bumper to thefront wheels of the vehicle, b₁ is the hitch length and b₂ is the lengthof the trailer, R_(f) is the turn radius of a front tip of the vehicle,and is determined as $\frac{l}{\delta},$ where δ is the steering angle.20. The method according to claim 18 further comprising displaying apath of the vehicle and a path of the trailer traveling around the curvefor the current steering angle and the desired steering angle.